'Limit selection to visible' suddenly not working in user perspective?
I think you are looking at it the wrong way...it is "limiting the selection to visible" (the verts up front) right now. It sounds like you want to disable it. Also you might want to fix your normals (Select All > Ctrl + N).

Let me clarify:


When the button is disabled you can "see through" it
When the button is enabled it appears opaque